Factor the following expression: $-5$ $x^2+$ $1$ $x+$ $18$
This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(-5)}{(18)} &=& -90 \\ {a} + {b} &=& & & {1} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $-90$ and add them together. Remember, since $-90$ is negative, one of the factors must be negative. The factors that add up to ${1}$ will be your ${a}$ and ${b}$ When ${a}$ is ${-9}$ and ${b}$ is ${10}$ $ \begin{eqnarray} {ab} &=& ({-9})({10}) &=& -90 \\ {a} + {b} &=& {-9} + {10} &=& 1 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {-5}x^2 {-9}x +{10}x +{18} $ Group the terms so that there is a common factor in each group: $ ({-5}x^2 {-9}x) + ({10}x +{18}) $ Factor out the common factors: $ x(-5x - 9) - 2(-5x - 9) $ Notice how $(-5x - 9)$ has become a common factor. Factor this out to find the answer. $(-5x - 9)(x - 2)$